1 / 20

Polynomial Basics: Introduction, Classification, and Arithmetic Operations

Learn the fundamentals of polynomials, including classifying based on terms, understanding monomials, binomials, and trinomials, calculating degrees, writing in standard form, plus adding and subtracting. Practice examples demonstrate operations and multiplication methods, guiding you through the key concepts. Develop a strong foundation in polynomial algebra starting from the basics.

acarlos
Download Presentation

Polynomial Basics: Introduction, Classification, and Arithmetic Operations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm UpIntroduction to Polynomials and Adding and Subtracting Polynomials

  2. Classifying Polynomials: We classify polynomials based on the number of _________. terms What is a monomial? A polynomial with only 1 term. What is a binomial? A polynomial with 2 terms. A polynomial with 3 terms. What is a trinomial? When do we use the term polynomial? We use the term polynomial to describe any expression which contains some combination of variables and numbers.

  3. What is a term? Terms are made up of numbers, variables or the product and/or quotient of some combination of numbers and variables. EXAMPLE: 2x is a term. (the product of a # and variable) 2x/3 is a term. (the quotient of a # and variable) - + Terms are separated by ________ and ________ signs!

  4. Classify each of the polynomials • 3x2y + 3x + 4y • 2x2y4z • 2xy2 + 3x2y + 9x • 5x2y + 2xy3 Trinomial Monomial Trinomial Binomial

  5. Calculating the degree of a polynomial.. If it is a single variable term, find the term with the largest exponent. 5x3 + 9x2 + x This is a 3rd degree polynomial. 1 Remember the understood 1!!! If it is a multi-variable term, you add the exponents of all of the variables. 4x2y + 2xy3 + 9 This is a 4th degree polynomial (3+1=4). Don’t forget the understood 1’s!!!! 1 1

  6. Calculate the degree of the polynomial… • 6x2 + 4x + 4x3 + x • 21x2y + 12x4y2 + 2xy4 • 3x2 + 2y3 3rd degree 6th degree 3rd degree

  7. Writing a polynomial in standard form… • Standard form is in descending order of the x variable. • 2xy3 + 3x2y + x3 • 3xy2 + 3x3 + 2x2y X3 + 3x2y + 2xy3 3x3 + 2x2y + 3xy2

  8. Adding and Subtracting Polynomials… is nothing more than combining like terms. Remember you can do this vertically or horizontally. • (2x2 - 3x + 3) + (4x2 + 5x - 9) • (3x2 - 9x - 5) - (-2x2 - 4x + 5) 6x2 + 2x -6 5x2 - 5x - 10 5(x2 - x - 2)

  9. Ex 1 (x2 + 3x + 4) + (-2x2 + 10x - 5) Combine LIKE terms x2 + 3x + 4 -2x2 + 10x - 5 -1x2 + 13x - 1 Final Answer

  10. Ex 2. (4b3 - 2b) + (b3 + 6b2 + 3b - 7) 4b3 + 0b2 - 2b + 0 b3 + 6b2 + 3b - 7 5b3 + 6b2 + 1b - 7 Final Answer

  11. Ex 3. (12y2 - 8y + 4) - (9y2 + 5y + 1) Don’t forget to Distribute the -1!! (12y2 - 8y + 4) - 1(9y2 + 5y + 1) (12y2 - 8y + 4) - 9y2- 5y - 1 12y2 - 8y + 4 - 9y2- 5y - 1 3y2 - 13y + 3 Final Answer

  12. Ex 4. (3a3 + 10a - 15) - (-a3 + 2a2 + 6a - 9) (3a3 + 10a - 15) - 1(-a3 + 2a2 + 6a - 9) 3a3 + 10a - 15 + a3 - 2a2- 6a + 9 3a3 + 0a2 + 10a - 15 +a3 - 2a2 - 6a + 9 4a3 - 2a2 + 4a - 6 Final Answer

  13. POLYNOMIAL MULTIPLICATION (2x - 3)(x + 5) 3 methods • Distribute (2x - 3)(x + 5) *4 multiplications 2x2+ 10x- 3x - 15 (then combine like terms) 2x2+ 10x - 3x - 15 2x2 + 7x - 15 Final Answer

  14. b. 3rd grade style 2x - 3 x + 5 +10x - 15 2x2 - 3x + 0 2x2 + 7x - 15 Final Answer!

  15. c. Box Method 2x - 3 x 2x2-3x + 5 +10x -15 2x2 + 7x - 15 Final Answer

  16. Ex 5. (4x + 7)(3x + 7) a.) 12x2+ 28x+ 21x + 49 12x2 + 49x + 49 b.) 4x + 7 c.) 4x + 7 3x + 7 3x 12x2 +21x +28x + 49 + 7 +28x + 49 12x2 + 21x + 0 12x2 + 49x + 49

  17. Ex 6. (x - 1)(x2 - 4x + 6) • x3- 4x2+ 6x - 1x2+ 4x- 6 x3 - 5x2 + 10x - 6 b. x2 - 4x + 6 c. x2 - 4x + 6 x - 1 x x3 -4x2 +6x -1x2 + 4x - 6 -1 -1x2 +4x - 6 1x3 -4x2 + 6x + 0 x3 - 5x2 + 10x - 6 x3 - 5x2 + 10x - 6

  18. Ex 7. (2z2 + 3z - 4)(4z + 5) • 8z3+ 10z2+ 12z2 + 15z - 16z- 20 8z3 + 22z2 - 1z - 20 b. 2z2 + 3z - 4 c. 2z2 + 3z - 4 4z + 5 4z 8z3 +12z2 -16z +10z2 + 15z - 20 +5 10z2 +15z - 20 8z3 +12z2 - 16z + 0 8z3 + 22z2 - 1z - 20

  19. Ex 8. (2a + 5)(2a - 5) • 4a2- 10a+ 10a - 25 4a2 - 25 b. 2a + 5 c. 2a +5 2a - 5 2a 4a2 +10a -10a - 25 -5 -10a -25 4a2 +10a + 0 4a2 - 25 4a2 - 25

  20. Ex 9. (3m + 4n)2 • (3m + 4n)(3m + 4n) 9m2+ 12mn+ 12mn + 16n2 9m2 + 24mn + 16n2 b. 3m + 4n c. 3m +4n 3m + 4n 3m 9m2 +12mn +12mn + 16n2 +4n +12mn +16n2 9m2 + 12mn + 0 9m2 + 24mn + 16n2 9m2 + 24mn + 16n2

More Related